The present invention relates to analog to digital to analog signal conversion, and more particularly to correcting quantization loss during such a conversion.
FIG. 1 is a block diagram illustrating a conventional analog to digital to analog signal conversion system 10. As is shown, an analog signal 20 is inputted into an analog to digital converter 12, where the analog signal is converted into a digital discrete time signal 22. A digital system 14 utilizes the digital signal 22 in such a manner that is well known to those skilled in the art, e.g., for storage, delay, etc., and is not germane to the present invention. The digital discrete time signal 22 is converted back into a reconstructed analog signal 24 by a digital to analog converter 16. The resulting reconstructed analog signal 24 can be passed through a low pass filter 18 to filter out quantization noise before the signal 24 is finally outputted as an analog signal 26.
Ideally, the analog signal out 26 is identical to the analog signal in 20. Quantization losses, however, inherently occur during the conversion process. In particular, quantization losses occur when the analog signal 24 is being reconstructed from the digital discrete time signal 22. This quantization loss is known as a xe2x80x9c(sin X)/x loss,xe2x80x9d and is reflected as a diminished energy amplitude for the signal.
The (sin x)/x loss is a function of how often the digital signal 22 is sampled in order to reconstruct the analog signal in 20. At lower frequency bandwidths of the digital signal 22, it is not difficult to select a sampling frequency that allows the digital to analog converter 16 to collect enough data points to accurately reconstruct the analog signal in 20. Thus, at lower frequency bandwidths, the quantization loss is negligible.
At higher frequency bandwidths, however, the sampling frequency is not high enough to accurately capture the true nature of the signal. For instance, if the sampling frequency is only twice the upper frequency of the high frequency bandwidth, the converter 16 will attempt to reproduce the upper frequency based on only two sampled data points. The converter 16 can only estimate the nature of the signal between the two points, and oftentimes underestimates the amplitude peak of the signal. Consequently, the quantization loss can be significant and the high frequency bandwidth of analog signal out 26 will not be an accurate reproduction of the same bandwidth of the analog signal in 20.
Accordingly what is needed is a system and method for correcting quantization loss during analog to digital to analog signal conversion. The system and method should provide an acceptable degree of accuracy of correction, but not require excessive processing power. The present invention addresses such a need.
The present invention provides a method and system for correcting quantization loss of a signal during analog to digital to analog signal conversion, wherein the quantization loss is a function of (sin x)/x. The system and method of the present invention includes utilizing a continuous function polynomial to represent a (sin x)/x function, and applying an inverse function of the continuous function polynomial to the signal to provide a correction for the quantization loss.
By utilizing a continuous function polynomial, such as McLaurin""s polynomial, to represent the (sin x)/x function, the correction for the quantization loss can be calculated quickly and easily, thereby expending little processing power. Moreover, a filter that creates an inverse function of the continuous function polynomial leaves a small footprint because it does not require significant hardware resources. If a sampling frequency is at least four times an upper frequency of a desired frequency bandwidth, only the first two members of the polynomial need be used to accurately approximate the quantization loss. Accordingly, under these conditions, the correction is accurately provided by creating an inverse function of only the first two members of the polynomial.